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They include romance between man and woman here and there, and some of them are indeed significant to the story, but they are romantic more because of their romantic nature.

By that broader definition of romance both Mouryou no Hako and Yakushiji Ryoko no Kaiki Jikenbo might qualify, though the latter is probably too comedic to really fit the OP's request. Mouryou no Hako opens with a "class-S" relationship between two adolescent girls and later includes the attraction between the detective and the ex-actress.

@Ellie
If you decide you might want to watch Mouryou no Hako, send me a PM or look for it via Google. The show is archived at a site I cannot link to here because it contains torrents for licensed shows as well.

Blood+ definitely fits your category. Fighting monsters, mysterious past, and beautiful romance. Both the male and female lead are very cool and strong. It has a nice ending too despite all of the shocking revelation and tragic moments.

High School of the dead is also a great example of horror anime. Fighting zombies and a nice love story.

Le Portrait de Petit Cossette is a good horror, tragic romance genre too, but the manga is much better.

If you want a mind screwing horror anime, then I think Aoi Bungaku is a great one.

EDIT: Oh one more suggestion: Boogiepop Phantom
This one has a very dark and creepy atmosphere, confusing psychological theme, disturbing strange plot yet charming and fascinating. I need to remind you though, it's pretty mind boggling and twisted, so stay away if you're younger than 18 years old.